Maurits Cornelis Escher (or simply M.C. Escher) was born in Leeuwarden,
Holland in 1898. He was never a good student during his childhood days.
The whole of his school days was a nightmare, the only saving grace
was his weekly 2 hour art lessons. Although he was considered by his
art teacher for having a more than average talent for art, Escher scored
a lowly seven. His art was not highly thought of by the examiners. Little
did they know that Escher would eventually become a famous artist for
creating higly imaginative artwork that marries the world of art and
mathematics.
In
his later years, he recalled his childhood days and wrote:
At
high school in Arnhem, I was extremely poor at arithmetic and algebra
because I had, and still have, great difficulty with the abstractions
of numbers and letters. When, later, in stereometry [solid geometry],
an appeal was made to my imagination, it went a bit better, but in school
I never excelled in that subject. But our path through life can take
strange turns
Despite
having no formal training in mathematics, Escher created artwork
that followed certain mathematical principles. His works included
exploration of the 3 dimensional world, perspective, abstract mathematical
solids, approaches to infinity and also the focus of this paper
– the art of creating tessellations.
Tessellations
are arrangements of closed shapes that completely cover the plan without
overlapping and leaving gaps.
Escher was fascinated by all types of tessellations, regular and irregular,
and he himself questioned the domain in which tessellations fell under:
mathematics or art?
He wrote:
“In mathematical quarters, the regular division of the plane
has been considered theoretically . . . Does this mean that it is an
exclusively mathematical question? In my opinion, it does not. [Mathematicians]
have opened the gate leading to an extensive domain, but they have not
entered this domain themselves. By their very nature they are more interested
in the way in which the gate is opened than in the garden lying behind
it."
Mathematics has shown that there are only three regular shapes that
can be used for a tiling. Escher exploited these basic patterns in his
tessellations, and applied principles of translations, glide reflections
and rotations to obtain a wide variety of patterns. The effects of his
tessellations are usually both astounding and beautiful.
The
Art Of The Alhambra
Escher’s
fascination with tessellations, or periodic drawing division began
when he briefly visited Alhambra, Spain in 1926. He was greatly
inspired and tried to emulate a rhythmic theme on a plane surface
himself. However, he was frustrated by his attempts to do so,
as he could only produce some ugly, rigid four legged beasts which
walked upside down on his drawing paper. It was only during the
second visit in 1937 that he began a more serious study into the
art of creating tessellations.
He
was fascinated by the rich possibilities latent in the rhythmic
division of a plane surface found in Moorish tessellations. He
and his wife studied these artworks deeply and Escher finally
came up with a complete practical system that he applied in his
later artworks of metamorphosis and cycle prints.
Escher's
Sketch of the tessellations in Alhambra, Spain
Our
Area of Focus
As
Escher's works cover many areas from perspective distortions to metamorphoses,
as such we felt that to talk a little about everything would have been
explaining too little of too many things. As such, we have singled in
onto one particular type of his work, tessellations.
In
addition, the team felt that it we wanted to keep our explanations simple
and clear, as such the extensive use of Flash animation is was chosen
as the medium to relay our thoughts.
Aim
We hope to achieve through this paper:
-a
deeper understanding and appreciation of Escher’s tessellations
-to uncover the underlying mathematical principles behind his artwork
-based on principles that we have learned, we will also attempt to create
some original tessellations of our own
-lastly, to explore the possibilities of his artwork in practical usage
in areas of architecture such as space, form and façade treatment.
